Field

History of Science, History of Mathematics

Research Interests

My research illuminates the deep interconnections between mathematics and its social, cultural, and political setting. Critical mathematical developments, I have found, were inseparable from broader historical trends that motivated them and gave them meaning and purpose. And quite often, major cultural and political developments cannot be fully understood without their mathematical context.

Infinitesimal (2014), my latest book, is the story of the mathematical concept of the infinitely small, which in the 17th century became a battleground of competing visions of modernity. Those who believed that the only solution to the religious and political crisis of the age was the establishment of an unchallengeable fixed hierarchical order admired Euclidean geometry and denounced the novel and paradoxical infinitesimal methods. In contrast, many supporters of the new approach championed pragmatism over dogmatism and pluralism over a single all-encompassing hierarchical order. The opposite results of the struggle in England and Italy held profound implications for their respective paths to modernity.

My first book, Geometrical Landscapes (2002), demonstrates how early modern geometers came to view their field as a hazardous voyage of exploration on the seas of mathematics. This new vision of the field in turn made possible the emergence of the new infinitesimal mathematics, leading to the development of the calculus. Duel at Dawn: Heroes, Martyrs, and the Rise of Modern Mathematics (2010), focuses on the role of stories in the emergence of the modern practice of mathematics in the 19th century. It demonstrates how higher mathematics as it is practiced today is inseparable from the enduring figure of the mathematician as a tragic romantic hero.

Notes

Education

Stanford University
1996 Ph.D. in History of Science
1990 M.A. in History of Science

The Hebrew University in Jerusalem
1988 B.S. in Mathematics and History

Selected Publications

Books

Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World (New York: Farrar, Strauss, and Giroux / Scientific American, 2014).

Duel at Dawn: Heroes, Martyrs, and the Rise of Modern Mathematics, (Cambridge MA: Harvard University Press, 2010). Reissued in paperback, 2011.

Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice (Stanford: Stanford University Press, 2002). Recipient of the Choice magazine Outstanding Academic Title Award for 2003.

Selected Publications

“Mathematics, 1770-1914” in Kapil Raj and Otto Sibum eds., The History of Modern Science (Paris: La Seuil, 2014) forthcoming.

“Examining the Square Root of D’oh!,” review of Simon Singh, The Simpsons and their Mathematical Secrets (New York: Bloomsbury USA, 2013), New York Times, January 27, 2014.

“From Voyagers to Martyrs: Towards a Storied History of Mathematics,” in Apostolos Doxiadis and Barry Mazur eds., Circles Disturbed: The Interplay of Mathematics and Narrative (Princeton: Princeton University Press, 2012).

“The Skeleton in the Closet: Should Historians of Science Care about the History of Mathematics?” introduction to a focus section on the history of science and the history of mathematics, Isis, vol. 102, no. 3, September 2011.

“Hariot and Dee on Geographical Exploration and Mathematics: Did Scientific Imagery Make for New Scientific Practice?” in Brett D. Steele and Tamera Dorland eds., The Heirs of Archimedes: Science and the Art of War Through the Age of Enlightenment, (Cambridge: MIT Press, 2005).

“Stories and Numbers: How a Romantic Tale of Geographical Exploration Transformed Mathematics,” Historically Speaking: The Bulletin of the Historical Society, January 2004.

“Mathematics,” in Jonathan Dewald ed., From Gutenberg to the Bastille: The Emergence of the Modern World, (New York: Scribner, 2003).

Alongside our existing 12 sub-fields, the History Department supports a number of cross-field clusters. The clusters are intended to attract students and faculty to important themes and current in the historical discipline. The clusters will offer new courses, sponsor outside speakers, and convene Department-based workshops and seminars.